Solve frac{sqrt{2}-sqrt{3}}{sqrt{11}}

$$\frac { \sqrt { 2 } - \sqrt { 3 } } { \sqrt { 11 } }$$

Evaluate

$$\frac{\sqrt{22}-\sqrt{33}}{11}\approx -0.095831535$$

Solution Steps

Rationalize the denominator of \frac{\sqrt{2}-\sqrt{3}}{\sqrt{11}} by multiplying numerator and denominator by \sqrt{11}.

$$\frac{\left(\sqrt{2}-\sqrt{3}\right)\sqrt{11}}{\left(\sqrt{11}\right)^{2}}$$

The square of \sqrt{11} is 11.

$$\frac{\left(\sqrt{2}-\sqrt{3}\right)\sqrt{11}}{11}$$

Use the distributive property to multiply \sqrt{2}-\sqrt{3} by \sqrt{11}.

$$\frac{\sqrt{2}\sqrt{11}-\sqrt{3}\sqrt{11}}{11}$$

To multiply \sqrt{2} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\sqrt{22}-\sqrt{3}\sqrt{11}}{11}$$

To multiply \sqrt{3} and \sqrt{11}, multiply the numbers under the square root.

$$\frac{\sqrt{22}-\sqrt{33}}{11}$$